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STA107 Lectures 18 & 19 Negative Binomial Distribution

STA107 Lectures 18 & 19 Negative Binomial Distribution. Bernoulli trial Experiment has 2 outcomes, success or failure, P(S) = p Define RV X; X is # Successes, x= 0 or x=1 E(X) = p Var (X) = p(1-p). Geometric Distribution Conduct iid Bernoulli trails until a S occurs

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STA107 Lectures 18 & 19 Negative Binomial Distribution

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  1. STA107 Lectures 18 & 19Negative Binomial Distribution Bernoulli trial Experiment has 2 outcomes, success or failure, P(S) = p Define RV X; X is #Successes, x= 0 or x=1 E(X) = p Var(X) = p(1-p)

  2. Geometric Distribution • Conduct iidBernoulli trails until a S occurs • Define RV X; X = #Trials; x= 1, 2, 3, …. • pmf: • E(X) = 1/p • Var(X) = (1-p)/p2

  3. Example An intersection you pass on the way to school has a traffic light that is green for 40sec and then amber or red for a total of 60sec. What is the probability that Friday is the first day the light is green for you this week? Ans: 0.05184

  4. Negative Binomial Distribution • Conduct iidBernoulli trails until k Successes have occurred • Define RV X; X = #Trials; x= k. k+1, k+2, …. • pmf: • E(X) = k/p • Var(X) = k(1-p)/p2

  5. Example An oil company conducts a geological study that indicates that an exploratory oil well should have a 20% chance of striking oil. What is the probability that the first strike comes on the third well drilled? Ans: 0.128 What is the probability that the third strike comes on the seventh well drilled? Ans: 0.049

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